1. Field of the Invention
The present invention relates to a method and an apparatus for analyzing a correlation for semiconductor chips; a semiconductor chip yield adjusting method using the same; and a storage medium for storing program for carrying out the analyzing method. The correlation may be one between the good or defective product ratio of semiconductor chips and a monitored quantity which is a physical quantity in the semiconductor chips or a state quantity of an apparatus for producing semiconductor chips. The correlation may be another one between a geometrically physical quantity of a device in the semiconductor chips, which is a kind of monitored quantity, and an electrically physical quantity which is a kind of monitored quantity in the semiconductor chips.
2. Description of the Related Art
A method for analyzing a correlation for semiconductor chips has become an important technology in order to improve the product yield of mass-produced semiconductor chips in a short period.
Even though semiconductor chips are mass-produced with various kinds of established conditions of a semiconductor chip manufacturing process, the concentration of impurities, wiring width and film thickness are made uneven due to variation of practical conditions, thus product yield thereof may change. Therefore, an quantity X pertaining to semiconductor chips or the production thereof is monitored, and data of sets of the monitored quantity X and yield Y are collected, wherein the data are statistically analyzed in order to determine a correlation between the monitored quantity X and yield Y. Thereby, the monitored quantity X is made to change so as to improve the yield Y.
In the literature, Allan Wong, "Statistical Micro Yield Modeling", Semiconductor International, November 1996, p.139-148, the following method for analyzing a correlation with respect to semiconductor chips is disclosed.
In FIG. 10, n wafer data (Xj, Yj), for j=1 through n, of sets of the monitored quantity X and yield Y are obtained for n wafers 11 through 1n, wherein Xj is the mean value of electrical test results with respect to a plurality of semiconductor chips on the wafer 1j.
Yj includes a random yield component Yr caused by, for example, defective short circuiting between conductors due to contamination. Since the random yield Yr has no relation to the correlation between the monitored quantity X and yield Y, it is necessary to eliminate the random yield Yr by separating the random yield Yr from non-random components (systematic yield) Ys. The following equation; EQU Y=Yr*Ys, Yr=EXP(-S*D) (1)
is established, where S is the area of a chip, D is a defect density which means the number of defects per unit area, and * is a multiplying operator.
The following equation can be obtained from the above equation (1). EQU Log(Y)=Log(Ys)-S*D (2)
Since Ys and D do not depend on the value of S, If S can be changed, Log(Y) becomes log(Ys) at S=0 on a straight line expressing a relationship between Log(Y) and S, thereby Ys can be obtained. In order to calculate yield Y, it is assumed that i chips adjacent to each other is a hypothetical chip having an area S=i*A, wherein if any one of the i chips is defective, the hypothetical chip is regarded as defective.
For example, in FIG. 11(A), it is assumed that rectangles marked with a cross `X` are defective chips. Y=72/75 if S=A. If S=3A, for example, it is assumed that, sets (4, 5, 6), (2, 5, 8), (2, 5, 4), (4, 5, 8) and (8, 5, 6) of three chips including chip 5 and adjacent to each other are all independent hypothetical chips different from each other.
As shown in FIG. 11(B), the relationship between S and Log(Y) is linearly approximated by the least square method in order to obtain a systematic yield Ys.
Thus, with respect to each of the yields of Y1 through Yn of wafers 11 through 1n in FIG. 10, from which the random yield is separated, and the systematic yields Ys1 through Ysn are obtained.
A scatter diagram of monitored quantity X to systematic yield Ys becomes as shown, for example, in FIG. 13, wherein since dots are scattered, the correlation between the monitored quantity X and the systematic yield Ys is unclear. This is because only one monitored quantity X is taken into consideration although the systematic yield Ys depends on many parameters. Simultaneously taking many parameters into consideration, the correlation may be made clearer. However, since there are parameters which are not measured or those which are difficult to measure, the correlation may not be made completely clear. Furthermore, since semiconductor chips are produced through a number of processes and the number of parameters is more than 100, it is not easy to know that which parameters should be changed and how much they should be changed in order to increase yield.
In the above-mentioned literature, the following process is performed to solve this problem.
(1) As shown in FIG. 12, wafer data (X1,Ys1) through (Xn, Yn) are sorted in ascending numeric order of the systematic yield Ys and are classified into four wafer groups #1 through #4 so that the number of data in the respective groups becomes approximately the same. This corresponds to dividing the number of data into four along the dashed lines parallel to the X-axis in a dispersion view of FIG. 13.
(2) The central values Q1 through Q4 are, respectively, obtained from the wafer groups #1 through #4. The central values Q1 through Q4 are the mean value or the median.
(3) A correlation coefficient between the monitored quantity X and systematic yield Ys is obtained with respect to only the central values Q1 through Q4 of the wafer groups. If the correlation coefficient value is more than a predetermined value, it is regarded that the correlation between the monitored quantity X and the systematic yield Ys is intensive.
(4) The above-mentioned processes (1) through (3) are carried out with respect to a number of monitored quantities X. By selecting only the monitored quantity X for which the correlation is regarded to be intensive in (3), the number of parameters is decreased, and a multiple regression equation of the systematic yield YS with respect to the selected monitored quantities is obtained.
However, when a regression line RLq about the central values Q1 through Q4 of the wafer groups thus obtained is determined, the inclination thereof is rather large. In a case where the regression line RLq is parallel to the systematic yield axis Ys, it is considered that the systematic yield Ys is in no relation to a change of the monitor value X. Therefore, even though it is attempted to increase the systematic yield Ys by changing the monitored quantity X on the basis of the regression line RLq having such greater inclination, the purpose may not be achieved in general. That is, with a prior art method for analyzing a correlation for semiconductor chips, it is possible to grasp, at a low degree of certainty, how the systematic yield changes when the monitored quantity is changed. Furthermore, the reliability of a correlation coefficient between the monitored quantity and the systematic yield is low. This is the same in cases where, instead of the systematic yield Ys, other good or defective product ratio such as a systematic defective product ratio (1-Ys), the yield Y from which Ys is not yet separated or a defective product ratio (1-Y) are used.